Quantum computing is accomplished using the effects of qubits that exhibit quantum mechanical behavior. A qubit is a physical system that is restricted to two or more energy states. A qubit is a quantum bit, the counterpart in quantum computing to the binary digit or bit of classical computing. Just as a bit is the basic unit of information in a classical computer, a qubit is the basic unit of information in a quantum computer. A qubit is conventionally a system having two or more discrete energy states. The energy states of a qubit are generally referred to as the basis states of the qubit. The basis states of a qubit are termed the |0> and |1> basis states. Typically, in quantum computing applications, a qubit is placed (e.g., biased) to a state where two of the discrete energy states of the qubit are degenerate. Energy states are degenerate when they possess the same energy.
A qubit can be in any superposition of two basis states, making it fundamentally different from a bit in an ordinary digital computer. A superposition of basis states arises in a qubit when there is a non-zero probability that the system occupies more than one of the basis states at a given time. Qualitatively, a superposition of basis states means that the qubit can be in both basis states |0> and |1> at the same time. Mathematically, a superposition of basis states means that the overall state of the qubit, which is denoted |Ψ>, has the form|Ψ>=a|0>+b|1>where a and b are coefficients respectively corresponding to probability amplitudes |a|2 and |b|2. The coefficients a and b each have real and imaginary components, which allows the phase of qubit to be modeled. The quantum nature of a qubit is largely derived from its ability to exist in a superposition of basis states, and for the state of the qubit to have a phase.
If certain conditions are satisfied, N qubits can define a state that is a combination of 2N classical states. This state undergoes evolution, governed by the interactions that the qubits have among themselves and with external influences, providing quantum mechanical operations that have no analogy with classical computing. The evolution of the states of N qubits defines a calculation or, in effect, 2N simultaneous classical calculations. Reading out the states of the qubits after evolution completely determines the results of the calculations.
It is held by some in the art that certain quantum computing algorithms, such as the Shor algorithm, require that the number of qubits in the quantum computer must be at least 104. See Mooij et al., 1999, Science 285, p. 1036, which is hereby incorporated by reference in its entirety. Qubits have been implemented in cavity quantum dynamic systems, ion traps, and nuclear spins of large numbers of identical molecules. However, such systems are not particularly well suited for the realization of the desired high number of interacting qubits needed in a quantum computer. A survey of the current physical systems from which qubits can be formed is Braunstein and Lo (eds.), Scalable Quantum Computers, Wiley-VCH Verlag GmbH, Berlin (2001), which is hereby incorporated by reference in its entirety. Of the various physical systems surveyed, the systems that appear to be most suited for scaling (e.g., combined in such a manner that they interact with each other) are those physical systems that include superconducting structures such as superconducting qubits.
A proposal to build a scalable quantum computer from superconducting qubits was published in 1997. See Bocko et al., 1997, IEEE Trans. Appl. Supercon. 7, p. 3638, and Makhlin et al., 2001, Rev. of Mod. Phys., 73, p. 357, which are hereby incorporated by reference in their entireties. Since then, many designs have been introduced. One such design is the persistent current qubit. See Mooij et al., 1999, Science 285, 1036; and Orlando et al., 1999, Phys. Rev. B 60, 15398, which are hereby incorporated by reference in their entireties.
A description of the persistent current qubit, as described in Mooij et al., is illustrated by circuit 700 in FIG. 7. Circuit 700 consists of a loop with three small-capacitance Josephson junctions (702-1, 702-2, and 702-3) in series. In operation, circuit 700 encloses a magnetic flux fM0. Here, M0 is the superconducting flux quantum h/2e (i.e., fluxon, flux quantum) where h is Plank's constant and e is elementary charge. See Tinkham, Introduction to Superconductivity, McGraw-Hill, Inc., New York, 1996, which is hereby incorporated by reference in its entirety, for a theoretical description of the fluxon. In operation, the magnetic flux fM0 enclosed by circuit 700 is created by applying an external magnetic flux with magnitude fM0 to circuit 700. This external magnetic flux is referred to as an applied magnetic flux, applied magnetic frustration, or simply frustration flux. Two of the junctions 702 in circuit 700 have equal Josephson coupling energies Ej. The Josephson coupling energy of the third junction 702 is less than the coupling energy Ej of the first two junctions 702. Typically, the Josephson energy of the third junction 702 is αEj, with 0.5<α<1.
An important feature of the Josephson energy in circuit 700 is that it is a function of two phases. For a range of frustration fluxes fM0, where f represents some range of numbers, these two phases permit two stable configurations that correspond to dc currents flowing in opposite directions. In fact, for f=0.5 (i.e., 0.5×M0, one half a fluxon), the energies of the two stable configurations (states) are the same (are degenerate). Thus, when an external magnetic force having the magnitude fM0 (where f=0.5) is applied against circuit 700, the circuit acts as a persistent current qubit with two degenerate states. One of the degenerate states, represented by a clockwise dc current 720 circulating in circuit 700, may be arbitrarily assigned the basis state |0>. Then the other degenerate state, represented by a counterclockwise dc current 722 circulating in circuit 700, is assigned the basis state |1>. Another property of circuit 700 is that the barrier for quantum tunneling between the two degenerate states depends strongly on the value α. Larger values α (i.e., higher Josephson energy in the third junction 702) result in higher tunneling barriers.
One advantage of superconducting qubits is that they are scalable. A disadvantage of persistent current qubit 700 is that it is difficult to provide a stable source for the applied magnetic flux fM0 that is necessary to produce the two degenerate states. Fluctuations in the frustration flux can decohere the states of the qubit making computation difficult or unreliable. Decoherence is the loss of the phases of quantum superpositions in a qubit as a result of interactions with the environment. Thus, decoherence results in the loss of the superposition of basis states in a qubit. See, for example, Zurek, 1991, Phys. Today 44, p. 36; Leggett et al., 1987, Rev. Mod. Phys. 59, p. 1; Weiss, 1999, Quantitative Dissipative Systems, 2nd ed., World Scientific, Singapore; Hu et al; arXiv:cond-mat/0108339, which are herein incorporated by reference in their entireties. Inductance from normal electronics is not suitable for producing degenerate states in a persistent current qubit. Any disruption in the current through such electronics will disrupt the degenerate states. Vibrations of the system can cause a change in the level of frustration (level of bias). Even the briefest interruption in the degeneracy of the states will destroy the quantum computation performed on the qubit.
One approach to trap flux is through flux quantization in a ring of superconducting material that has a cross section that is larger than the London penetration depth λL. In this approach, an external flux of about one flux quantum is applied to ring while cooling the ring down through the superconducting phase transition. Once below the superconducting phase transition temperature, the center of the ring (the aperture of the ring) will have a magnetic flux of one flux quantum because it will be trapped by the surrounding superconducting material. Then, the external field is removed. When the external magnetic field is removed in a nonsuperconducting ring, the magnetic flux in the center of the ring pierces the ring and is annihilated. However, this is not possible in a superconducting ring because the magnetic flux trapped in the center of the ring cannot penetrate the superconducting ring. Thus, in this way, a ring is capable of trapping magnetic field in multiples of the magnetic flux quantum (i.e., 1×h/2e, 2×h/2e, 3×h/2e, and so forth). The flux is quantized because the wavefunction of the supercurrent is naturally single valued. This means the integral of the phase around the ring of superconducting material should be a multiple of 2π.
One possibility for providing an applied magnetic flux to a persistent current qubit is a superconducting ring recently proposed by Majer et al. See Majer et al., 2002, Applied Physics Letters 80, p. 3638 which is hereby incorporated by reference in its entirety. Majer et al. proposed a mesoscopic (e.g., having a diameter of 3 μm) superconducting ring 800 (FIG. 8) that has no junctions. A superconducting material is a material that has zero electrical resistance below critical levels of current, magnetic field and temperature. The Majer et al. ring has a cross section 802 that is narrower than the London penetration depth λL of the ring. The London penetration depth λL describes the exponentially decaying magnetic field in layers just below the surface of a superconductor. In general, magnetic fields are excluded within superconducting materials. The exclusion of magnetic fields deep in a superconducting material is known as the Meissner effect. However, in shallow layers just below the surface of superconducting materials, the extent to which magnetic fields are excluded is exponentially dependent on the distance between the layer and the surface of the superconductor. The London penetration depth λL of a superconducting material is the distance from the material surface to a point in the material where magnetic flux is e−1 times less than at the material surface. Here, e is the base of the natural logarithm. London penetration depth is material dependent but typically on the order of 500 Å for some superconducting materials.
As mentioned above, the ring proposed by Majer et al. has a cross section 802 that is narrower than the London penetration depth λ of the ring. However, the ring 800 can be used to trap magnetic flux through the phenomena of fluxoid quantization, which is a distinctly different phenomena than the phenomena of flux quantization described above. The difference between flouxoid quantization and flux quantization is that, although the resultant magnetic field is the same, the origins of the magnetic field differ. In flux quantization of a thick ring, the magnetic field in the ring is comprised of a trapped magnetic field. In fluxiod quantization of a ring that is narrower than the London penetration depth of the ring, the magnetic field in the ring is induced by circulating current that remains in the ring. See M. Tinkham, 1996, Introduction to Superconductivity, McGraw Hill, which is hereby incorporated by reference in its entirety. In one approach, an external flux quantum is applied to ring 800 while cooling the ring down through the superconducting phase transition. The center of ring 800 will have a magnetic flux quantum because of the presence of the external magnetic flux. Then, once ring 800 is superconducting, the external field is removed. When the external magnetic field is removed in a nonsuperconducting ring, the magnetic flux in the center of the ring pierces the ring and is annihilated. However, this is not possible in the ring proposed by Majer et al. because the magnetic flux is induced in the center of the ring by superconducting current in the ring. A superconducting ring is capable of trapping magnetic field in multiples of the magnetic flux quantum (i.e., 1×h/2e, 2×h/2e, 3×h/2e, and so forth). The magnetic field is comprised of the trapped flux and the flux generated by the circulating current. The Majer et al. ring provides no mechanism for releasing trapped magnetic flux. The trapped magnetic flux can be used as a source for applying a stable magnetic field to a persistent current qubit. The trapped magnetic flux in the Majer et al. ring is advantageous because it is not sensitive to fluctuations in applied current. In fact, no applied current is required to maintain the trapped magnetic flux in the Majer et al. ring 800 once it has been trapped in the aperture of the ring.
While ring 800 represents a significant achievement in the art, it does not provide a satisfactory device for applying an external biasing (frustrating) magnetic field to a persistent current qubit for two reasons. First, ring 800 does not provide a mechanism for trapping or releasing trapped magnetic flux. The only way to trap or release the trapped magnetic flux in ring 800 is to destroy the superconducting properties of the ring. This can be accomplished, for example, by raising the temperature of the ring through the critical temperature TC of the superconducting material used to manufacture the ring. Second, ring 800 is not capable of trapping sub-fluxon quantities of magnetic flux. That is, ring 800 is not capable of trapping a magnetic flux having a magnitude that is a fraction of h/2e. Yet, many persistent current qubits, such as circuit 700, require an external magnetic force having a magnitude that is a fraction of a fluxon in order to achieve two degenerate states.
Given the above background, what is needed in the art is a mechanism for delivering a stable and switchable flux source with sub-fluxon precision.
Discussion or citation of a reference herein shall not be construed as an admission that such reference is prior art to the present invention.